Sets of numbers have been formed in logical order. [color=#0000ff]Natural numbers[/color] express quantity. When our ancestors noticed, that decrease of quantity can be expressed with negative numbers, they had the set of [color=#0000ff]integers[/color]. Integers can be used, for example, to express the numbers roundings or time before and after present. [br][br]Integers were followed by [color=#0000ff]rational numbers (or fractions)[/color]. In the past, time may have been given as [i]half of moon[/i]. Babylonians divided the circle and year to 360 parts, as it had many factors: 1, 2, 3, 4, 5, 6, 9, 10, 12,...This enabled them to solve many things exactly. [color=#0000ff]Rational numbers can be either finite or infinite.[/color] [br][br]The circle gave new dimensions to the numbers. It was found, for example, that circumference of a circle cannot be solved exactly only with a radius and an angle. The missing part [math]\Large \pi[/math] is not a rational numbers but [color=#0000ff]infinite and non-recurring decimal number,[color=#000000] that is[/color] irrational number. [color=#000000]Rational numbers and irrational numbers are called as [color=#0000ff]real numbers[/color].[/color][/color] [br]    [br]Mathematically set of numbers are symbolized as[br][br][math]\Large\textcolor{blue}{\cal N = \{0,\,1,\,2,\ldots \}}\\[br]\Large\textcolor{blue}{\cal Z = \{\ldots,\,-1,\,-1,\,0,\,1,\,2,\,\ldots\}}\\[br]\Large\textcolor{blue}{\cal Q=\{\frac{m}{n}|m,n\in \cal Z,\; n\neq0\} }\\[br]\Large\textcolor{blue}{\cal R \Large\text{ all other real numbers besides previous, like } \pi,\,\sqrt 2,\,\sqrt[3] 5,\;\ldots}\\[br]\Large \textcolor{blue}{\cal C \Large\text{ is set of complex numbers. They are in a form of }\Large a+bi \text{, where } a,b\in R \text{ and } i^2=-1} [/math][br][br]Complex numbers are used in electrical engineering and in solving differential equations. Computationally, it can be seen, when, for example, the inner part of a square root is negative [math]( \sqrt{-4} = 2i).[/math] For complex numbers [math] i^2=-1.[/math]